Conventional proportional derivative (PD) type controllers are widely used in industry even in some of the most advanced controllers due to the simplicity and proven stability of the PD controllers.
The use of a PD type controller does not effectively handle steady state errors which are derived, for example in a hydraulic robot, from the flow deadband nonlinearity due to control valve (spool valve) deadband, friction resisting spool displacement, robot joint friction and load.
The use of proportional integrated derivative type controls (PID) are reasonably effective in eliminating some steady state errors but are generally ineffective with respect to overshoot wherein the end point of the robot travels beyond its intended target.
U.S. Pat. No. 4,777,303 issued Feb. 23, 1988 to Morse et al. describes a specific system for applying an offset signal to a controller to compensate for steady state error and provide a faster settling time for controlling dynamic manipulators such as robots. In this system the offset signal comprises the integration of the position error weighted by a function of the angular shaft velocity. This system is only active when the load velocity is so low when sticking is imminent.
Morse et al. specifically pertains to controllers where the rate varying factor goes to zero as the velocity approaches infinity, therefore, the system of Morse et al does not reset to zero on velocity reversal, and is not effective in ensuring proper tracking of the end point along the selected trajectory.